Stats Help Needed Badly!!?

Question

Conduct the appropriate hypothesis test, using alpha= .05, to determine if there is a difference in the 1) variances and 2) the means between the two machines.
MODEL A:
Mean4.962131148
Standard Deviation0.09516853
SAMPLE Variance0.009057049
Sum302.69
Count61

MODEL B:
Mean4.999836066
Standard Deviation0.077663629
SAMPLE Variance0.006031639
Sum304.99
Count61

Ok, so I need to know how I find out if there is a difference in the variances and the means of the two models. I am confused on what test to use (z, t, etc...)? Can anyone show me how to do this, Please Help!!

Answer 1

Dear S S,

I'm not a statistics expert, but here is my understanding of the common procedure.

1) To test if there is a statistical difference in variances, I think you take their ratio (dividing the larger by the smaller), then compare that value with a table of F. There is 1 degree of freedom between the two machine models, and 120 degrees of freedom within the models (61 - 1 for each). The variance ratio is around 1.50, which is less than 3.9 in the F table for alpha = 0.05, so the variances do not appear to differ significantly.

2) I think a Student's t-test is what you would use for a statistical difference in the means. Since you already have sample variances (call them vA and vB), compute the variance of their difference as

vD = vA / nA + vB / nB = 0.00906 / 61 + 0.00603 / 61 = 0.000247,

where nA = nB = 61 are the counts you have from each machine.

Let sD = (vD)^0.5 = 0.0157 be the standard deviation of the difference between the means, and

let mD = | mB - mA | = 0.0377 be the absolute value of the difference between the two sample means, mA and mB.

Then you can form t as

t = mD / sD = 2.40 .

Now you can compare this t value with a t table (not to be confused with a coffee table...sorry, I couldn't resist), using alpha = 0.05 and 120 degrees of freedom (based on your counts, as in question 1). The t table shows 1.98, and since your calculated value of t = 2.40 > 1.98, the means appear to be significantly different.

(As a footnote, I believe that the t-test is only valid if the variances for the two machine models are similar. Since the first question indicated that the variances did not differ significantly, the t-test in the second question should be valid.)